When two identical springs are connected in parallel, the effective spring constant is given by the equation:
1/k_parallel = 1/k1 + 1/k2
where k1 and k2 are the spring constants of the individual springs.
When another identical spring is connected in series to the parallel combination, the effective spring constant is given by the equation:
k_series = k_parallel + k3
where k3 is the spring constant of the additional spring.
To find the least friction required to pull a body of weight W, we need to determine the maximum force that can be applied without exceeding the static frictional force.
The static frictional force can be calculated using the equation:
f_friction = μ * N
where μ is the coefficient of static friction and N is the normal force.
The normal force N is equal to the weight of the body W.
Now, let's simplify the problem by assuming that the weight W is applied vertically downwards and the force is applied at an angle with the horizontal. In this case, the effective weight acting in the horizontal direction is W * sin(θ), where θ is the angle at which the force is applied.
To find the least friction required, we need to determine the maximum horizontal force that can be applied without exceeding the static frictional force. This maximum force is given by:
F_max = μ * N = μ * W
Therefore, the least friction required is μ * W.
However, since the force is applied at an angle with the horizontal, the effective weight acting in the horizontal direction is W * sin(θ). Therefore, the least friction required is:
Friction = μ * W * sin(θ)
Find the least friction required to pull a body of weight W placed on a rough horizontal plane, winen the force is applied at an angle with the horizontal.
(a) Two identical springs connected in parallel are in series arrangement with another identical spring.
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